With 18 strength and a quarterstaff, you can hit regular zombies hard enough to explode them. I think you’re forgetting that base damage for melee weapons is modified by strength, but this is not the case for ranged weapons. A greatbow doing 35 damage is slightly more than a 9mm pistol that I can loot off a zombie on day one without building my entire character around it, and significantly less than a pipe rifle I can build with similar crafting skills, again using commonly loot able ammunition.
I still don’t understand why you think dumping dex and perc isn’t a flaw. There are a host of things your character gets worse at, and I have no idea how you figure you can get enough skills to compensate by the third day.